Focus: Quantum States Made to Order

Published June 23, 1998  |  Phys. Rev. Focus 1, 21 (1998)  |  DOI: 10.1103/PhysRevFocus.1.21

Measurement of the Amplitude and Phase of a Sculpted Rydberg Wave Packet

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum

Published June 22, 1998
Figure 1
Thomas Weinacht/University of Michigan

Designer wave packet. The height of this surface represents the wave function amplitude the authors measured for a Rydberg wave packet vs. the electron’s atomic position, with color indicating phase. (This wave packet includes the energy states with principle quantum numbers n from 25 through 32.)

Humans have always tried to tame nature, and for many atomic physicists, the dream is to completely control the quantum state of an atom or molecule. By manipulating atomic and molecular states researchers could prepare them for a wide range of physics experiments and perhaps even chemical reactions. In the 22 June PRL a team reports “sculpting” the quantum state of an atomic electron and then completely determining its wave function–the “probability wave” that describes the state. They specified the state with unprecedented detail using new laser technology and measured the wave function more completely and directly than previous experimenters.

Phil Bucksbaum, of the University of Michigan in Ann Arbor, and his colleagues have used several techniques to study quantum states by shooting laser beams at clouds of atoms. But Bucksbaum says they ran into trouble because the standard methods for probing atoms gave an incomplete picture of the shape and motion of the wave function. So he and his group devised a solution using Rydberg atoms, in which an electron is boosted to an orbit far from the nucleus, and the available energy levels and quantum states are similar to those of a hydrogen atom.

The researchers used new laser pulse “shaping” technology to precisely tailor the frequency components of a 150 femtosecond pulse in order to excite the atoms into a specific set of eight energy states. They specified both the amplitude and phase of each energy state relative to the others, making a combination state called a “wave packet.” A short time later the atoms received a second, reference pulse that excited them into the same set of states but with different amplitudes and phases–the reference wave packet. Following such a pulse pair, the atoms are described by a combination of the wave packets from both pulses, and they interfere quantum mechanically, just as an electron can, in a sense, go through both slits of a double slit experiment and thus interfere with itself.

Because the electron of each Rydberg energy state in the set of eight has a slightly different average distance from the nucleus, the researchers can identify an electron’s energy level by the voltage required to strip it away from the atom. By ramping an applied voltage during a period of 2 microseconds, and measuring the number of electrons freed at each voltage, the team determined the atoms’ probability of being in each energy state. But they also used this energy spectrum in a new way: Since the spectrum came from the interference of two different, well-defined wave packets–which cancel or add depending on their relative phases–the researchers could derive the phase information from the data. For each of the eight energy states they found an amplitude and phase that agreed with the values they had tried to put into the wave packet with the shaped laser pulse at the outset.

Princeton University’s Warren Warren calls the work an “elegant experiment” and says it’s the first explicit measurement of the phase of an atomic wave packet. He also sees it from the laser technology point of view: “It’s a nice example of the potential applications now that we can treat optical fields with the same degree of control that we’ve had with radio waves for decades.”

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